Scotland produced four superb goals, with Kenny McLean netting from the halfway line and Scott McTominay scoring with an overhead kick.
Afterwards, Clarke beamed: "Really simple - what a fantastic group of players. Unbelievable.
"I've said it from the very start of my time. It took me a year, maybe 18 months, to work out the best way to go forward. If I give myself a bit of credit, I chose the right way.
"We chose more caps, more experience. When you come to a night like this, when you're behind and struggling, and not sure it's going to happen, I trust my players.
"I've told them so many times, I trust them implicitly.
"I woke up this morning, and as a manager you normally wake up with that tight feeling in your stomach. I didn't have it this morning, and I thought 'wow, that's strange.
"I thought there was something wrong with me! But it's because I trust my players so much."
Clarke also stated: "Scott McTominay scored the best overhead kick I've ever seen and it might not have been the best goal of the night!
"It was a lot of emotions. High and low. At times, you're looking for solutions and thinking how to change it. I knew at some stage we'd have to go two up front.
"I felt the Danes were dominating us a little. It seemed like a good time (to make the changes). Whether they were 10 or 11 (men), we were going to do that.
"I spoke to Kieran (Tierney) before the first game. He's a key player for me, one of my men. I've got loads of them. 14 were involved in the play-off game.
"I said 'listen, Aaron Hickey can't do back-to-back games, I can see you coming on at right-back and doing very well for us'.
"I'm not sure I envisioned the goal... but when it was rolling back to him on his left foot, I knew he would score.
"When (Kenny) hit it, I thought 'what are you doing?!' but when I saw it in flight, I thought 'that's going to go in!'"